An infinite geometric series has common ratio $\frac{-1}{3}$ and sum $25.$  What is the second term of the sequence?
The second term seems difficult to calculate directly, so we will first find the value of the first term. Let the first term be $a$.  Because the sum of the series is $25,$ we have  \[25= \frac{a}{1-\left(\frac{-1}{3}\right)} = \frac{a}{\frac{4}{3}} = \frac{3a}{4}.\]Thus, $a=\frac{100}{3}.$ Now, we can calculate the second term knowing the value of the first. The second term $ar$ is \[ar=\left( \frac{100}{3} \right)\left(\frac{-1}{3}\right)=\boxed{\frac{-100}{9}} .\]